It was collected in the Chacaico Sur locality from the Emileia giebeli ammonoid zone of the Los Molles Formation, Cuyo Group, dating to the early Bajocian stage of the Middle Jurassic, about 171.6-170 million years ago.

Mollesaurus, along with Chacaicosaurus cayi which was found at the same locality, are the only diagnostic ichthyosaur specimens from the Aalenian-Bathonian interval.

[3][4] Patrick S. Druckenmiller and Erin E. Maxwell (2010) found it to be the basalmost member of the ophthalmosaurid lineage that included Brachypterygius, Caypullisaurus and Platypterygius (but not Ophthalmosaurus).

[3] Valentin Fischer, Michael W. Maisch, Darren Naish, Ralf Kosma, Jeff Liston, Ulrich Joger, Fritz J. Krüger, Judith Pardo Pérez, Jessica Tainsh and Robert M. Appleby (2012) found it to be the basalmost member of Ophthalmosaurinae.

[6] Acamptonectes densus Mollesaurus periallus Ophthalmosaurus natans Ophthalmosaurus icenicus Gengasaurus nicosiai Nannopterygius yasykovi Nannopterygius enthekiodon Nannopterygius saveljeviensis Nannopterygius borealis Arthropterygius volgensis Arthropterygius lundi Arthropterygius thalassonotus Arthropterygius hoybergeti Arthropterygius chrisorum Brachypterygius extremus Aegirosaurus leptospondylus Muiscasaurus catheti Leninia stellans Sveltonectes insolitus Athabascasaurus bitumineus Platypterygius americanus Acuetzpalin carranzai Platypterygius sachicarum Caypullisaurus bonapartei Grendelius mordax Grendelius alekseevi Grendelius pseudoscythicus Grendelius zhuravlevi Undorosaurus kielanae Undorosaurus nessovi Undorosaurus gorodischensis Platypterygius australis Plutoniosaurus bedengensis Simbirskiasaurus birjukovi Platypterygius hercynicus Sisteronia seeleyi Platypterygius platydactylus Maiaspondylus lindoei